Yeah it's the latter. The US does not have party membership the way that, say, the UK does. In many states, it's open primary. In Colorado, for instance, I get mailed Democratic and Republican primary ballots and can vote by mailing in either one. I think you get neither counted if you mail in both, but I have no idea; I've never tried it.

The last time anyone tried to poison a presidential election by promoting a weaker candidate on the other side in the US, it was the Democrats boosting Trump in 2016. It did not work out.